The present invention generally relates to slide rule-like calculators and more particularly to a slide rule-like calculator and method for quickly and simply selecting appropriate spot-type fire detector devices and determining their preferred locations in rooms of varied size and ceiling characteristic. Such calculator and method permit a ready, direct-reading comparison of varied spot-type fire protective schemes for a space of specified dimension and ceiling type.
The National Fire Protection Association, particularly in NFPA Standard No. 72E, Automatic Fire Detectors (1974), has established space rating requirements for spot-type fire detectors and preferred room locations for their installation. These space ratings, the maximum linear spacings between similar detectors, are determined by standard testing agencies, such as Underwriters Laboratories, Inc., and Factory Mutual Laboratories, Inc., in actual fire tests.
For example, a detector to be rated is positioned at one corner of an imaginary square, whose center is the fire location. The response of this detector is then compared to that of an ordinary sprinkler (160.degree. F.) located at a similar corner of an imaginary 10 .times. 10 foot square about the central fire. The detector receives that rating, i.e. imaginary square size, at which it responds before the sprinkler to the heat of the central fire. Thus, detectors are rated on the basis of square patterns, e.g. a 30 ft. .times. 30 ft. detector, protects a smaller space division than a 40 ft. .times. 40 ft. detector.
As at least on smooth ceilings a fire spreads uniformly in all directions in an ever expanding circle, the actual protective coverage of a detector, rather than being an imaginary square of size S .times. S (space rating) is more correctly a circle circumscribed about the rating square. The diameter, D, of this fire protection circle, being the diagonal of the inscribed square, equals the square root of the sum of the square of the sides of the square in accordance with the following formula: EQU D = (S.sup.2 + S.sup.2).sup.1/2 = (2S.sup.2).sup.1/2 = S(2).sup.1/2
it is important to note that such uniformity of fire spread and detector response to a central fire on a smooth ceiling having no beams or obstructions greater than 4 inches deep is not applicable to more specialized ceiling types where the spread of the fire is inhibited by the obstructions. Rather, beamed ceilings, having beams 4-18 inches deep, spaced greater than 3 feet apart, center to center, and joisted ceilings, having solid joists deeper than 4 inches and spaced less than 3 feet apart, center to center, require derating of the smooth ceiling determined space ratings and diameters. Such space rating reductions equal in standard calculations to one-third for beamed ceilings and one-half for joisted ceilings, this spacing reduction factor being applied to the dimension perpendicular to the beams. Moreover, for ceilings with beams deeper than 18 inches, no derating is sufficient and each bay must be treated as a separate area. Hence, any determination of a fire protective scheme must be effected only after consideration of room size, ceiling type and standarized space ratings.
In that many rooms are rectangular vice square in dimension, it should be realized that any rectangle of diagonal dimension equal to or less than the diameter D of the above described circle or its derated value in the special ceiling cases also resides within the rated protective zone. Thus, such maximum diagonal, the square root of the sum of the square of the length (A) and width (B) of the rectangular space equals the fire protective circle's diameter (D), previously calculated from the imaginary square of the space rating (S .times. S). This dual relationship is expressed mathematically as follows: EQU D = S(2).sup.1/2 = (A.sup.2 + B.sup.2).sup.1/2
such commonality of relationship between a given space rating and a specific rectangular size permits the measurement rectangulation and derating as necessary of a chosen space. The actual comparison of these trial rectangles with the the various space rating squares affords a determination of which size and number of space divisions best satisfy the limits or capabilities of protection of the various spot-type fire detectors. This division and comparative procedure adduces the selection of an appropriate fire protective scheme for the actual room and ceiling type confronted.
Formerly, this comparative selection process has consisted of an operator or estimator subdividing the areas to be protected into convenient rectangles or squares; measuring or estimating the sides of those space divisions; derating as appropriate that side perpendicular to any obstructions; determining the length of the diagonal of the space division; and comparing such diagonals with those determined from the space ratings of particular fire detectors. This process, given the infinite number of rectangular combinations and ceiling types possible in a room and the myriad protective schemes warranted by such variables involved repeated calculation and reference to numerous charts to reach the most effective and economic fire protective detector mix. Such process being time-consuming, tedious, and prone to mistake, often resulted in less than a full utilization of a detector's rated protective coverage.